rotation spectra

1. D. JIM LIVINGSTON
FACULTY OF CHEMISTRY
ST. JOHN’S COLLEGE

2. MICROWAVE SPECTRA
• THIS SPECTROSCOPY UTILIZES PHOTONS IN THE MICROWAVE RANGE TO CAUSE
TRANSITIONS BETWEEN THE QUANTUM ROTATIONAL ENERGY LEVELS OF A GAS
MOLECULE.
• MICROWAVE REGION – 10-3 to 10-1m
•Why Gas Phase?
• INTERMOLECULAR INTERACTIONS HINDERING ROTATIONS IN THE LIQUID AND SOLID
PHASES OF THE MOLECULE.
•Condition
• Molecule must posses a permanent dipole moment.

3. DIPOLE MOMENT
• A DIPOLE MOMENT IS A QUANTITY THAT DESCRIBES TWO OPPOSITE CHARGES
SEPARATED BY A DISTANCE
• BY DEFINITION THE DIPOLE MOMENT, Μ, IS THE PRODUCT OF THE MAGNITUDE OF THE
SEPARATED CHARGE AND THE DISTANCE OF THE SEPARATION
When atoms in a molecule share
electrons unequally, they create what is
called a dipole moment.

4. WHICH MOLECULES EXHIBIT MICROWAVE
SPECTRA?
• HOMONUCLEAR DIATOMIC MOLECULES: MICROWAVE INACTIVE
• H2,O2, Cl2, CO2,C6H6 – ZERO DIPOLE MOMENT ( NO CHARGE SEPARATION)
• HETERONUCLEAR DIATOMIC MOLECULES: MICROWAVE ACTIVE
• HCl, HBr, CO, NO – PERMANENT DIPOLE MOMENT (CHARGE SEPARATION)
• SELECTION RULE:
• A SELECTION RULE, OR TRANSITION RULE, FORMALLY CONSTRAINS THE POSSIBLE
TRANSITIONS OF A SYSTEM FROM ONE QUANTUM STATE TO ANOTHER.
• SELECTION RULES HAVE BEEN DERIVED FOR ELECTROMAGNETIC TRANSITIONS IN
MOLECULES, IN ATOMS, IN ATOMIC NUCLEI, AND SO ON.
• FOR ROTATIONAL SPECTRA ΔJ = ±1.

5. DERIVATION OF THE EXPRESSION FOR ROTATIONAL
ENERGY
The rotations of a diatomic molecule can be
modeled as a rigid rotor.
The rigid rotor model has two masses attached
to each other with a fixed distance between
the two masses.
I – moment of inertia
ɷ - angular velocity

6. Assume a rigid (not elastic) bond
r0 = r1 + r2
Center of gravity, C :
m1r1 = m2r2
m1r1 = m2 (r0 - r1)
= m2r0 - m2r1
m2r0 = m1r1 + m2r1
m2r0 = (m1 + m2) r1
21
01
2
mm
rm
r



7. • THE MOMENT OF INERTIA
• I = Σ miri
2 ( ri - distance ith of particle of mass mi from cg)
• For diatomic particle , I = m1r1
2 + m2r2
2
• Substituting the values of r1 and r2,
• 𝑰 =
𝒎 𝟏
𝒎 𝟐
𝟐
𝒎 𝟏
+𝒎 𝟐
𝟐 𝒓 𝟐 +
𝒎 𝟏
𝟐
𝒎 𝟐
𝒎 𝟏
+𝒎 𝟐
𝟐 𝒓 𝟐
• I=
𝒎 𝟏
𝒎 𝟐
𝒎 𝟏
+𝒎 𝟐
𝒓 𝟐
• µ - reduced mass.
I = µr2

8. • ANGULAR MOMENTUM L = IW (W – ANGULAR VELOCITY)
• THE QUANTIZED ANGULAR VELOCITY IS GIVEN BY
• L = 𝐽 𝐽 + 1 h/2Π ( J= 0,1,2,3… ROTATIONAL Q. NO)
• ENERGY OF ROTATION
• Multiply and divide by I,
• E = (IW)2/2I
• E = L2 / 2I
• Sub. Value of L,
• E =
ℎ
2
8π
2
𝐼
𝐽 (𝐽+1)

9. • To express energy in cm-1,
• F(J) = E/ hc =
ℎ
8π2
𝐼𝑐
𝐽 (𝐽+1) cm-1
• F(J) – total rotational energy (rotational term)
• B – rotational constant
F(J) = BJ (J+1)
B =
h/8π2Ic

10. SELECTION RULE
• Transitions in which
rot. Q.No increase
or decrease by unity are allowed.
Transition from J to J+1,
Energy difference 𝚫E = EJ+1 – EJ
𝛎J J+1 = B(J+1)(J+2) – BJ(J+1)
= B(J2+3J+2) – B(J2+J)
= 2B(J+1)cm-1
J = 𝚫 ± 1
F(J) = BJ (J+1)

11. • 𝛎(0-1) = 2B
• 𝛎(1-2) = 4B
• 𝛎(2-3) = 6B
• 𝛎(3-4) = 8B
•
• J = 0 J = 2
FORBIDD
EN

13. DETERMINATION OF BOND DISTANCE